Arm with a combined shape and force sensor

ABSTRACT

A system comprises an arm including a bendable section and a force transmission mechanism. The system also comprises an actuation mechanism coupled to the force transmission mechanism to bend the bendable section. The system also comprises an electronic data processor configured to receive sensor data about the bendable section and determine external force information about at least one of a magnitude or a direction of an external force applied to the arm from the sensor data. the processor is also configured to determine a pose of the bendable section from the sensor data and generate control information for the actuation mechanism to maintain the pose of the bendable section in a stationary configuration as the external force is applied to or withdrawn from the arm.

BACKGROUND 1. Field of Invention

Aspects of the invention relate to a system for using a sensor tomonitor both the shape of an arm as well as an external force applied tothat arm. Some aspects of the invention are particularly suited formonitoring flexible guide tubes and articulated arms used in roboticsurgery.

2. Art

There has been considerable effort in developing systems for performingminimally invasive surgery. One area of particular interest isrobotically assisted surgery.

In robotically assisted surgery, the surgeon typically operates acontrol device at a location that is remote from the patient to controlthe motion of surgical instruments at the patient's surgical site. Thecontrol device typically includes one or more manually operated inputdevices, such as multiple degree of freedom master tool manipulators,joysticks, exoskeletal gloves, or the like, which are coupled to thesurgical instruments via servo motors for articulating the instrumentsat the surgical site. During the surgical operation, the control devicecontrols a surgical robotic manipulator that provides mechanicalarticulation and functional control of a variety of surgicalinstruments, such as tissue graspers, needle drivers, electrosurgicalcautery probes, etc., that each perform various functions for thesurgeon, e.g., holding or driving a needle, grasping a blood vessel,dissecting, cauterizing, or coagulating tissue.

Such systems typically include at least one arm having a plurality ofjoints that interconnect small links to provide articulation. Some formof control mechanism is provided to move the arm into various poses. Forexample, the control mechanism can include one or more tendons (e.g.,cables) running along the length of the arm. Tensioning one or more ofthe tendons causes the arm to bend at the joints. The tendons mayactively control the arm's bending and straightening. Alternatively, insome designs, each joint can be provided with a stiffening element(e.g., a spring) that provides a restoring force to return the arm to astraight orientation when tension on a tendon has been relaxed. Somepractical designs may contain multiple bending links per joint. In suchmultiple-link joints, the stiffening element controls how the multiplebending links bend in a coordinated fashion to form the complete joint.

Although there is a direct relationship between the amount of tensionplaced on the tendons and the resulting shape of the arm, mechanicaltolerances, drive train friction, tendon stretch, and other conditionsmay prevent one from determining the actual shape of the arm withsufficient precision if the determination is based solely on cabletension. Therefore, various efforts have been made to develop a systemto continuously monitor the actual shape of the arm as it moves during asurgical procedure.

One such monitoring approach is disclosed in U.S. Patent ApplicationPub. No. US 2007/0156019 A1 (filed Jul. 20, 2006)(the “'019Application”), which is incorporated herein by reference. This approachrelies on a fiber optic shape sensor. In this type of device, an opticalfiber is provided with a plurality of cores. Arrays of Bragg gratingsare formed along the core continuously or at spaced-apart locations.Each Bragg grating comprises a series of modulations of the core'srefractive index so as to generate a spatial periodicity in therefraction index. The spacing may be chosen so that the partialreflections from each index change add coherently for a narrow band ofwavelengths, and therefore they reflect only this narrow band ofwavelengths while passing a much broader band. During fabrication of thegratings, the modulations are spaced by a known distance, therebycausing reflection of a known band of wavelengths. When a strain isinduced on the fiber core, the spacing of the modulations will change,depending on the amount of strain in the core.

To measure strain, light is sent down the fiber, and the reflectedwavelength is a function of the strain on the fiber and its temperature.This fiber Bragg grating (FBG) technology is commercially available froma variety of sources, such as Smart Fibres Ltd. of Bracknell, England.When applied to a multicore fiber, bending of the optical fiber inducesstrain on the cores that can be measured by monitoring the wavelengthshifts in each core. By having two or more cores disposed off-axis(i.e., not coincident with the lengthwise center longitudinal axis) inthe fiber, bending of the fiber induces different strains on each of thecores. These strains are a function of the local degree of bending ofthe fiber. Regions of the cores containing FBGs, if located at pointswhere the fiber is bent, can thereby be used to determine the amount ofbending at those points.

The collected data, combined with the known spacings of the FBG regions,can be used to reconstruct the shape of the fiber. Such a system hasbeen described by Luna Innovations, Inc. of Blacksburg, Va.

The '019 Application describes how this technology can be used tomonitor the shape of a robotic arm. As discussed therein, a controlsystem can be provided for detecting the position of the surgicalinstrument and for utilizing that information to assist in surgicalprocedures. In one embodiment, the control system includes a detectionsystem and a servo controller. The detection system is utilized forgenerating and detecting the light used for determining the position ofthe instrument. The servo controller may utilize the positioninformation as feedback for positioning the instrument.

When using an articulated arm during surgery, it is also desirable toknow about any external forces placed on the arm, particularly externalforces applied at the distal tip. Information about the external forcesupon the arm can be fed back to the surgeon during the procedure tofacilitate the manipulation of the arm.

Various approaches have been developed for monitoring the externalforces placed upon an articulated arm. In one example, strain gauges areplaced on rigid portions of the arm. External forces induce strain inthe gauges that can be measured. Examples of the use of force sensors inrobotic arms can be found in the '019 Application, U.S. PatentApplication Pub. No. US 2008/0065111 A1 (filed Sep. 29, 2007), U.S.patent application Ser. No. 11/858,772, (filed Dec. 18, 2007), and U.S.patent application Ser. No. 12/060,004, (filed Mar. 31, 2008), allincorporated herein by reference.

SUMMARY

As noted above, when operating an articulated arm for robotic surgery,it is desirable that both the shape of the arm and external forcesacting upon the arm be known. The subject invention is based on therecognition that data generated by bend sensors can also be used, inmost circumstances, to derive information about external forces. Inparticular, the system must be of the type wherein the external forcedoes not influence the shape of the arm in the same direction as theinternal actuation or kinematic constraint forces. An example where thiscondition would be violated is when a force is directed against the tipof a straight arm along the longitudinal axis of the arm. In thissituation, (and assuming no measurable compression or buckling occurs)the external force would not affect the shape of the arm and could notbe measured. Where the external force causes the shape of the arm todeviate from the shape it would achieve based only on the cableactuation, however, the external force can be determined.

In accordance with an aspect of the invention, an articulated arm isprovided with one or more control tendons for changing the shape of thearm. In addition, the arm is provided with a plurality of bend sensors.In a preferred embodiment, the bend sensors are Bragg gratings formed onan optical fiber, as described in the prior art.

In use, the fiber optic bend sensors are interrogated in a mannersimilar to past ways. In the subject approach, however, data from theinterrogation is analyzed to derive both the internal actuation forceapplied to the arm as well as the external force acting on the arm.

As discussed below, aspects of the invention are applicable to systemsboth with and without stiffening elements.

Aspects of the invention are also generally applicable to flexibleprobes that do not include any internal actuation mechanisms. Forexample, bend sensors can be used with a flexible spring element tomonitor the shape of the element in response to an external force. Theinformation from the bend sensors can be used to compute the externalforce.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic view that illustrates a basic inventiveconcept.

FIG. 2 is a diagrammatic view of elements of an arm and the associatedforces that will be calculated in accordance with an aspect of thesubject invention.

FIG. 3 is diagrammatic view of one embodiment of the subject invention.

FIG. 4 is diagrammatic view of an articulated arm.

DETAILED DESCRIPTION

Arms, including instruments and structures used to support and move suchinstruments, may be substantially rigid or flexible. Flexibleinstruments may be classified into two types: (i) continuously flexiblearms that do not have discrete joints (i.e., infinite degrees offreedom), and (ii) arms that have a series of two or more short linksinterconnected by joints having at least one degree of freedom (thenumber of degrees of freedom being sufficient to provide the requiredflexibility). Many medical devices, such as catheters and small diameterminimally invasive instruments, have such a continuously flexibleproperty. Many other medical devices, such as relatively large diameterendoscopes that include one or more working channels for minimallyinvasive instruments, are made of such a series of short, interconnectedlinks. It is possible to have a hybrid flexible arm that includes atleast one continuously flexible portion and at least one link portion.Arms with both rigid and flexible (continuous, linked, or hybrid)portions are also possible.

Such arms may be actuated to move by various methods that provide anecessary actuation force. One exemplary method is actuation with one ormore tendons (e.g., cables) that run along the length of an arm. Apulling force (tension) in one or more of the tendons bends the arm or asegment in the arm. Actuation force may be provided from varioussources, such as manual crank or a servomotor. Other mechanicalactuation methods, such as providing pushing force (compression) ontendons, using gears, etc. are known and may be used.

An arm may include a passive stiffening element that applies a restoringforce to a default pose for the arm. Stiffening elements may be ofvarious forms, such as an internal spring that runs inside the flexiblearm or an external sheath that surrounds the flexible arm. When nobending forces are applied to such an arm, the stiffening elementenforces a minimum energy shape or kinematic configuration. If a bendingforce is applied to the arm, the stiffening element opposes the bendingforce on the portion of the arm that is being moved.

Both internal actuation force and external force may be applied to thearm. An example of an external force is the reactive force the armexperiences if it is pushed against tissue. The stiffening elementopposes both externally applied force and the internal actuation force.In addition to opposing the actuation force, the stiffening element alsospreads the actuation force across the bending portion of the arm sothat, for instance, the angle between each link in a series of links isabout equal.

It is possible to use a bend or shape sensor to detect not just thenominal bends associated with the normal actuation of the arm, but alsothe perturbation, generated by an external force, of the stiffeningelement away from its minimum energy shape. It is therefore possible todetect the magnitude and direction of the applied external force inaddition to the shape of the arm.

The subject invention can be implemented using fiber optic shape sensingtechnology of the type disclosed in the '019 Application, referencedabove. (See also, U.S. patent application Ser. No. 12/164,829, (filedJun. 30, 2008), which is incorporated by reference.) As discussed below,other shape sensing technologies could be used.

Aspects of the invention may be applied to several arm configurations.One illustrative configuration is to have a non-actuated continuouslyflexible arm with a stiffening element. A simple example of this firstillustrative configuration is the optical fiber bend sensor alone, sinceit is continuously flexible and possesses an inherent stiffness. Asecond configuration is to have an actuated continuous or discretelyflexible arm with a stiffening element. This second configuration, onwhich much of the following description is based, is underactuated,because actuation does not fully control the shape. A thirdconfiguration is to have an actuated discrete link flexible arm withoutan additional stiffening element. Since the stiffening element is notpresent in this third configuration, the arm's actuation mechanism mustbe able to completely determine the arm's kinematic position (i.e.,every degree of freedom is actuated). In each of these illustrativeconfigurations, the mechanical properties of these configurations (e.g.,dimensions (such as link size, distance between joints, fit tolerances,and the like), material properties (such as known or estimated friction,cable “stretchiness”, and the like), etc.) are known so that suchinformation can be combined with information from the sensor to derivethe actuation force and/or a force externally applied to the arm.

FIG. 1 illustrates a basic inventive concept. An arm is illustrated as atubular member 10, which includes an internal stiffening element (notshown). In pose 10 a, tubular member 10's curved shape is caused byinternal tensioning (actuation) forces. If a force F is applied to theend of the member 10 in pose 10 a, it will begin to bend in an “S” likeshape as illustrated by pose 10 b, since the internal stiffening elementmust deflect to create a restoring force equal to force F. If a shapesensor is used to measure the bend in member 10, the information itgenerates can also be used to measure the external force. In FIG. 1, Xrepresents the distance between the arm's minimum energy shape under theinternal actuation force and the arm's actual shape (the result of theexternal force). For stiffness matrix K that may depend upon X, F is theforce (F=KX).

FIG. 2 provides a more detailed example. In this example, the elongatearm 200 is attached at one end (the proximal end) to a fixed, knownposition 202. The position of the distal end 204 is determined by anumber of forces acting on the arm. First, the arm contains a stiffeningelement that provides forces that restore the arm to a certain preferredshape. Second, some actuation mechanism (e.g., a servo actuator)actively influences the shape of the arm. Finally, an external force isapplied at the distal end 204 of the arm. The total shape of the arm ismeasured by a sensing apparatus (not shown).

As shown in FIG. 2, the elongate arm 200 is a planar device composed ofthree rigid links L (links L may be relatively short, to form a flexibleconfiguration that approximates a continuously flexible arm, or they maybe relatively longer). Two revolute joints 206 a couple the ends of thelinks L in series, and a third revolute joint 206 b couples the proximalend of the arm to base 202. The axes of the revolute joints areparallel, so that the arm articulates in a plane (x-y, as shown). Thestiffening element is a combination of three equal torsional springs S,each with stiffness k, that are attached at each joint 206. Theactuation mechanism is a single cable C attached at the distal tip 204and routed along the links, and the sensing apparatus (not shown)measures the angles of the three joints 206. The external force f is alinear force in the arm's plane of motion that is applied at the distaltip, as illustrated by the arrow.

The three forces (stiffness, actuation, external) act at differentlocations and in different ways on the arm, but the forces can becompared by writing a force balance for the torques applied at each ofthe three joints. For a general arm with 11 joints, standard roboticstheory and geometry are used to make this force balance:

0=τ=Wu−Kθ+Bf

where τ is the total combined n-dimensional torque vector, which shouldbalance to zero if the system is not moving, u is the c-dimensionalvector of cable forces, θ is the n-dimensional vector of joint angles,and f is the e-dimensional vector of external tip forces. In otherwords, n is the number of mechanical degrees of freedom, c is the degreeof actuation, and e is the number of independent external forcedirections. For the example in FIG. 2, (n,c,e)=(3,1,2), and the matricesW, K, and B are:

$\mspace{20mu} {W = \begin{bmatrix}{w\; {\cos \left( \theta_{1} \right)}} \\{w\; {\cos \left( \theta_{2} \right)}} \\{w\; {\cos \left( \theta_{3} \right)}}\end{bmatrix}}$ $\mspace{20mu} {K = \begin{bmatrix}k & 0 & 0 \\0 & k & 0 \\0 & 0 & k\end{bmatrix}}$ $B = {- {l\begin{bmatrix}\begin{matrix}{{\cos \left( \theta_{1} \right)} + {\cos \left( {\theta_{1} + \theta_{2}} \right)} +} \\{\cos \left( {\theta_{1} + \theta_{2} + \theta_{3}} \right)}\end{matrix} & \begin{matrix}{{\sin \left( \theta_{1} \right)} + {\sin \left( {\theta_{1} + \theta_{2}} \right)} +} \\{\sin \left( {\theta_{1} + \theta_{2} + \theta_{3}} \right)}\end{matrix} \\{{\cos \left( {\theta_{1} + \theta_{2}} \right)} + {\cos \left( {\theta_{1} + \theta_{2} + \theta_{3}} \right)}} & {{\sin \left( {\theta_{1} + \theta_{2}} \right)} + {\sin \left( {\theta_{1} + \theta_{2} + \theta_{3}} \right)}} \\{\cos \left( {\theta_{1} + \theta_{2\;} + \theta_{3}} \right)} & {\sin \left( {\theta_{1} + \theta_{2} + \theta_{3}} \right)}\end{bmatrix}}}$

The force balance equation can be used to determine the unknown externalforces f by measuring the shape θ of the arm. The approach assumes thatexternal tip forces f influence the shape differently than the (unknown)cable forces u, such that if sufficient shape variables θ are available(i.e., n is large enough), u and f can be recovered at the same time.

The force balance equation can be used to recover both the externalforce f and the actuation force u, provided that sufficient shapeinformation is available and the actuation and external forces influencethe shape independently. For the example of FIG. 2 and similartendon-actuated arms, these conditions are met unless the system is at akinematic singularity.

The force balance can be rewritten, separating the known from theunknown variables, as follows:

${\begin{bmatrix}W & B\end{bmatrix} \cdot \begin{bmatrix}u \\f\end{bmatrix}} = {K\; \theta}$

If the matrix [W B] has full column rank c+e (this is the mathematicalformulation of the condition “independent shape influence”), the unknownvariables u and f can be uniquely recovered, for example using apseudo-inverse as:

$\begin{bmatrix}u \\f\end{bmatrix} = {{\begin{bmatrix}W & B\end{bmatrix}^{+}K\; \theta} = {{\left( {\begin{bmatrix}W^{T} \\{B^{T}\;}\end{bmatrix} \cdot \begin{bmatrix}W & B\end{bmatrix}^{- 1}} \right)\begin{bmatrix}W^{T} \\B^{T}\end{bmatrix}}K\; \theta}}$

Intuitively, the way the force information is obtained is by comparingthe measured shape to a shape that could be achieved using only cableactuation. For example, without external forces, the system in FIG. 2will acquire a circular shape with all angles θ, equal, and solving theprevious equation will return a solution (u, f) with f=0. If θ describesa shape that is not a circle, then the equation translates this“non-circle” shape to external forces f that must have caused it.

Finally, it is important to note that this derivation relies on thefacts that the arm is only partially actuated (c<n), only certainexternal forces are applied (e<n), and the shape measurement is richenough to independently describe both effects (c+e<n). These dimensionalrelations, plus the condition that the matrix [W B] must have fullcolumn rank, can be used to generalize to more complex mechanisms.

It should be understood that the more degrees of freedom of movement inthe system, the easier it is to mathematically derive the externalforces on the system (the best case, therefore, is with the infinitedegrees of freedom of a continuously flexible arm). The example abovealso focused on recovering an external force applied to the distal tip.It should be understood that depending on the structure of the arm,external force(s) applied between the distal and proximal ends couldalso be determined. And, if sufficient shape information is available,an external force component directed along the arm's longitudinal axiscan be determined.

FIG. 3 is a schematic diagram of another illustrative embodiment of thesubject invention. In this illustration, the arm is a minimally invasivesurgical instrument 300 that includes an elongated, hollow,substantially rigid shaft 302 coupled at its distal end to a flexiblewrist section 304. A surgical end effector 306, such as a tissuegrasper, is connected to the distal end of the wrist section. A forcetransmission mechanism 310 is coupled to the proximal end of the shaft.Teleoperated servomotor actuators engage the transmission mechanism 310at mechanical interface 311, which in turn passes actuating forcesthrough shaft 302 via cables (not shown) to cause the wrist sectionmechanism to bend in pitch and/or yaw and to actuate the end effector.(See U.S. Pat. No. 6,817,974 (filed Jun. 28, 2002), U.S. Pat. No.5,807,377 (filed May 16, 1997), and U.S. Pat. No. 6,461,372 (filed Mar.8, 2000), each of which is incorporated herein by reference, for moredetails about this type of structure).

In accordance with an aspect of the subject invention, the instrument300 is illustratively provided with an optical fiber 312 that includes aplurality of fiber Bragg gratings for sensing shape. Fiber 312 extendsthrough wrist 304 and optionally into some or all of end effector 306.Information about these types of fibers is described in detail in theabove-cited patent applications. Other bend sensors could be used. Forexample, other optical fiber shape sensing technologies that do notrequire FBGs (e.g., Rayleigh scattering methods) may be used.Magnetic/electric field sensors can be placed along the length of theflexible arm. Alternatively, piezo sensors can be placed at the jointsor distributed along body of the arm. Other sensing possibilitiesinclude the use of sliding sensing cables that provide positioninformation of joints, or the use of three-dimensional imaging andmachine vision approaches to derive instrument position, orientation,and shape. Image-based tool tracking technology may also be used. (Seee.g., U.S. Patent Application Publications No. US 2009/0088897 A1 (filedSep. 30, 2007), US 2009/0088773 A1 (filed Sep. 30, 2007), and US2009/0088634 A1 (filed Sep. 30, 2007), each of which is incorporatedherein by reference.)

The proximal end of fiber 312 is coupled to fiber straininterrogator/detector unit 314. Unit 314 functions to send light downthe fiber and to collect and measure reflected light. As noted above,changes in the shape of the wrist 304 strain the gratings associatedwith the wrist, which in turn will change the character of the returnedlight in a manner which can be measured.

The output of unit 314 is supplied to an electronic data processor 316.Processor 316 uses the information to determine both the shape of thearm as well as any external forces applied to the arm as discussedabove. The external force information may then be used in ateleoperation loop to output an indication of the forces haptically at amaster control device (e.g., finger or hand grip), or to output theforce indications to the user in some other way (e.g., using visual,vibro-tactile, etc. methods). (See, U.S. Pat. No. 6,424,885, (filed Aug.13, 1999) incorporated herein by reference.) The external forceinformation may also be routed in a control loop to a controller 318that automatically controls one or more of the servomotor actuators tokeep instrument 300's arm stationary as the external force is applied toor withdrawn from the arm. The shaft 302 and wrist 304 arm configurationis illustrative of various arm configurations as described above.

FIG. 4 illustrates another type of robotic arm 400 that could be adaptedfor use with the subject invention. Arm 400 includes a plurality ofspaced apart disks 402. Each of the disks 402 is rigidly attached to acenter spine 404. The center spine exerts a spring (stiffening) forcethat attempts to straighten arm 400 if bent.

Each of three tendons 406 are rigidly attached to the most distal disk402 and pass through holes in the remaining disks. Arm 400 is notconstrained to planar movement, and it is actuated by changing therelative tension among the three tendons. In free space, the arm willbend in a smooth arc so as to minimize the energy stored in the centerspine. If a force is applied to the arm, however, its shape will changein a manner that can be measured. As with the embodiment of FIG. 3, theembodiment of FIG. 4 is provided with an apparatus as described abovefor monitoring the change in shape of the arm. One suitable apparatuswould be an optical fiber with Bragg gratings, as discussed above.

The ability to recover both the tendon forces and the external forcesacting on a movable arm can be used to control the arm. For example,with this information, the control system (FIG. 3) can be programmed tocompensate for various drive train dynamics, for example, frictionacting on actuation cables.

Referring now to the first illustrative configuration mentioned above inparagraph 0027 (non-actuated continuously flexible arm with a stiffeningelement), the approach for determining external forces using bendsensors can be applied to flexible probes that contain no actuatingmechanisms for internally controlling the motion of the probe. In asimple example, the probe can be a spring element having bend sensorsapplied thereto. When the distal tip of the probe hits a surface, itwill bend into some shape. The bend sensors can be used to determinethat shape. The information about the shape can be used to determine theforce vector applied to the tip. This concept can apply to a probe withinfinite degrees of freedom, such as a continuously flexible device orto a device with a finite number of degrees of freedom. An illustrativeprobe is a whisker-like device that has a known, inherent stiffness.

In the prior art, strain gauges have been mounted on rigid links of anarm to determine some information about lateral forces on the arm thatcause shaft bending and shear loads. In the case of the flexible probediscussed above, however, the interest is in deriving bend informationthat modifies the shape of the probe rather than strain information.Such bend information can be derived using the Luna fiber systemmentioned above.

Referring now to the third illustrative condition referred to inparagraph 0027 (actuated discrete link flexible arm without a stiffeningelement), the subject invention can also be used with robotic arms thatare fully actuated with no explicit stiffening elements. Informationabout external forces can be derived by using the bend sensors todetermine how the links deflect (since the links will, in fact, havefinite stiffness). In this system, the bend sensor information from thelinks is used to determine force, and the bend sensor information fromthe joints is used to determine joint position. Both force and jointposition information are usable in a control system, as illustratedabove.

In another aspect, it can be seen that a similar approach may be usedfor sensing twist force around a longitudinal axis (i.e., the axisbetween proximal and distal ends) of an arm. The combination of anoptical fiber that is used to sense twist (e.g., a four core fiber withone core aligned with the fiber's longitudinal axis and the other threecores equidistantly spaced around the center core) and a torsion springthat seeks a minimum torsional energy state may be used to determinetorque on the linkage arm or continuously flexible arm. The torquesensing multicore fiber may also be used to sense bend, and also lateralforce, as described above.

While the subject invention has been described with reference to severalembodiments, various changes and modifications could be made therein, byone skilled in the art, without varying from the scope and spirit of thesubject invention as defined by the appended claims. Principles andelements illustrated in one or more of the drawings or described abovein relation to one aspect, embodiment, or implementation of theinvention are not limited solely to that one aspect, embodiment, orimplementation, but may be incorporated in various other aspects,embodiments, and implementations. For example, shape sensor apparatuscomponents and electronic data processors that receive informationextracted from shape sensor apparatus components may be incorporated asnecessary in the various aspects, embodiments, and implementationsillustrated and described herein.

1-19. (canceled)
 20. A system comprising: an arm including a bendable section and a force transmission mechanism; an actuation mechanism coupled to the force transmission mechanism to bend the bendable section; and an electronic data processor configured to receive sensor data about the bendable section, determine external force information about at least one of a magnitude or a direction of an external force applied to the arm from the sensor data, determine a pose of the bendable section from the sensor data, and generate control information for the actuation mechanism to maintain the pose of the bendable section in a stationary configuration as the external force is applied to or withdrawn from the arm.
 21. The system of claim 20 further comprising: a stiffening element for providing a restoration force to the arm.
 22. The system of claim 20 wherein the sensor data includes shape data about the bendable section.
 23. The system of claim 20 wherein the pose of the bendable section is further determined from information representing at least one mechanical property of the arm.
 24. The system of claim 20 further comprising: an end effector coupled to the bendable section of the arm.
 25. The system of claim 24 wherein the actuation mechanism is coupled to the force transmission mechanism to actuate the end effector.
 26. The system of claim 20 further comprising a sensor apparatus that generates the sensor data about the bendable section.
 27. The system of claim 26 wherein the sensor apparatus includes an optical fiber.
 28. The system of claim 20 wherein the bendable section of the arm includes a plurality of rigid links.
 29. The system of claim 20 wherein the bendable section of the arm is continuously flexible.
 30. A method comprising: receiving sensor data about a bendable section of a manipulator arm, the manipulator arm including a force transmission mechanism controlled by an actuation mechanism; determining, from the sensor data, external force information about at least one of a magnitude or a direction of an external force applied to the arm; determining a pose of the bendable section from the sensor data; and generating control information for the actuation mechanism to maintain the pose of the bendable section in a stationary configuration as the external force is applied to or withdrawn from the arm.
 31. The method of claim 30 wherein the arm includes a stiffening element and determining the pose of the bendable section includes combining the sensor data with restoration force information for the stiffening element.
 32. The method of claim 30 wherein the sensor data includes shape data about the bendable section.
 33. The method of claim 30 wherein the pose of the bendable section is further determined from information representing at least one mechanical property of the arm.
 34. The method of claim 30 further comprising: generating control information for the actuation mechanism to actuate an end effector coupled to the bendable section of the arm.
 35. The method of claim 34 further comprising operating the force transmission mechanism to actuate the end effector.
 36. The method of claim 30 further comprising receiving the sensor data about the bendable section from a sensor apparatus.
 37. The method of claim 36 wherein the sensor apparatus includes an optical fiber.
 38. The method of claim 30 wherein determining the pose of the bendable section from the sensor data includes determining the pose of a plurality of rigid links comprising the bendable section.
 39. The method of claim 30 wherein determining the pose of the bendable section from the sensor data includes determining the pose of a continuously flexible portion of the bendable section. 